《航海学》课程参考文献（地文资料）CHAPTER 15 NAVIGATIONAL ASTRONOMY

235NAVIGATIONALASTRONOMYStates.Otherbodiesriseobliquelyalongtheeasternhorizon,ZetthNoris PoleeslintieeNDecinatiee 23's-器Caliestia EquatoWorirse贷SouftNerthPolePileedination60rNaoSouthPoleFigure 1516a.The right sphere.Figure1516b.Theparallel sphere.ZonithZerNNHortzorCvi7NauticaltAsironon.NaditFigure1516c.Theoblique sphereat latitude40°NFigure 1516d.The various twilight at latitude 20°Nandlatitude60°N.climb to maximum altitude at the celestial meridian, and setwhy days and nights are always about the same length in thealongthe westemhorizonThe lengthoftimeabovethehorizonand the altitude at meridian transit vary with both the latitude oftropics,andthechangeoflengthofthedaybecomesgreatertheobserverandthedeclinationofthebody.Atthepolarcirclesas the latitude increases.It also explains why twilight lastsoftheeartheven the sunbecomes circumpolar.This isthelandlonger in higher latitudes.Twilight is theperiod of incom-ofthemidnight sun, where the sun does not setduringpart oftheplete darkness following sunset and preceding sunrisesummer and does not rise during part of the winter.Evening twilight starts at sunset,and morningtwilightendsThe increased obliquity at higher latitudes explainsatsunrise.Thedarkerlimitoftwilightoccurswhenthecen-

NAVIGATIONAL ASTRONOMY 235 States. Other bodies rise obliquely along the eastern horizon, climb to maximum altitude at the celestial meridian, and set along the western horizon. The length of time above the horizon and the altitude at meridian transit vary with both the latitude of the observer and the declination of the body. At the polar circles of the earth even the sun becomes circumpolar. This is the land of the midnight sun, where the sun does not set during part of the summer and does not rise during part of the winter. The increased obliquity at higher latitudes explains why days and nights are always about the same length in the tropics, and the change of length of the day becomes greater as the latitude increases. It also explains why twilight lasts longer in higher latitudes. Twilight is the period of incom￾plete darkness following sunset and preceding sunrise. Evening twilight starts at sunset, and morning twilight ends at sunrise. The darker limit of twilight occurs when the cen￾Figure 1516a. The right sphere. Figure 1516b. The parallel sphere. Figure 1516c. The oblique sphere at latitude 40°N. Figure 1516d. The various twilight at latitude 20°N and latitude 60°N

236NAVIGATIONALASTRONOMYter of the sun is a stated number of degrees below thenauticalandastronomicalcelestialhorizon.Threekindsof twilightaredefined:civil.TwilightAtdarkerlimitLighter limitDarkerlimitcivil0°50-6°Horizonclear,brightstarsvisible0°50-12°nauticalHorizon not visible-18°0°50Full nightastronomicalThe conditions at the darker limit are relative and varyrainthatappearstocomefromaheadduetotheobserver'sownconsiderablyunderdifferentatmosphericconditionsforwardmotion.TheapparentdirectionofthelightrayfromIn Figure 1516d, the twilight band is shown, with thethestar is the vector difference of the motion of lightand thedarker limits of the various kinds indicated.The nearlyver-motionoftheearth,similartothatofapparentwindonamov-ingvessel.This effect is most apparent for a bodytical celestial equator line is for an observer atlatitudeperpendicular to the line of travel of the earth in its orbit, for20oN.Thenearlyhorizontal celestial equatorlineis for anwhich it reaches a maximumvalue of20.5".The effect of ab-observerat latitude60°N.Thebrokenlinein eachcaseisthe diurnal circle of the sun when its declination is 15°Nerration can benoted bycomparingthe coordinates(declination and sidereal hour angle)of various stars through-The relativeduration of anykind of twilight at the two lat-itudes is indicated by the portion of the diurnal circleout the year.A change is observed in some bodies as the yearprogresses, but at the end ofthe year the values have returnedbetween the horizon and the darker limit, although it is notalmosttowhattheywereatthebeginning.Thereasontheydodirectlyproportionaltotherelativelength of lineshownsince the projection is orthographic.The duration of twi-notreturnexactlyisduetopropermotionandprecessionoftheequinoxes. It is also dueto nutation,an irregularity in the mo-light at the higher latitude is longer,proportionally,thanshown.Note that complete darkness does not occurat lati-tionoftheearthduetothedisturbingeffectofothercelestialtude60°Nwhen thedeclinationof the sun is15°N.bodies,principallythemoon.Polarmotion isa slightwobblingoftheearthabout itsaxisofrotationandsometimeswanderingofthepoles.Thismotion,whichdoesnotexceed40feetfrom1517.Apparent Motion Due To Revolution Of Thethemeanposition,produces slightvariation of latitude andEarthlongitudeofplacesontheearth.If itwerepossibletostoptherotationof theearthso1518.Apparent Motion Due To Movement Of Otherthatthecelestial sphere wouldappear stationary,theeffectsCelestial Bodiesof therevolutionof theearth would becomemorenotice-able.In one year the sun would appear to make onecompletetrip around the earth,from westto east.Hence,itEven if itwerepossibletostopboththerotation andwouldseemtomoveeastwardalittlelessthan1°perdayrevolution of the earth, celestial bodies would not appearstationary on the celestial sphere.The moon would makeThis motion canbe observed by watching the changing po-sition of the sun among the stars.But sinceboth sun andonerevolution about theeartheachsidereal month,rising instars generallyare not visible at the same time,a better waythe west and setting in the east.The inferior planets wouldis to observe the constellations at the same time each night.appeartomoveeastwardandwestwardrelativetothesunstaying within the zodiac.Superior planets would appeartoOnanynighta starrises nearlyfourminutesearlierthan onmake one revolution around the earth, from west to east,the previous night.Thus, the celestial sphere appears toshiftwestward nearly1each night, so that different con-eachsiderealperiod.stellations are associated with different seasons oftheyear.Since the sun(andthe earth with it)and all other stars areApparent motions ofplanets and themoon are duetoainmotionrelativetoeach other,slowapparentmotionscombinationoftheirmotionsandthoseoftheearth.Ifthero-would result in slightchanges in the positions ofthe starsrel-tation of the earth were stopped, the combined apparentativetoeachother.This spacemotion is,infact,observedbymotion dueto the revolutions of theearth and other bodiestelescope.The component of such motion acrossthe lineofwould be similarto thatoccurring if both rotation and revolu-sight, called propermotion,produces a change in the appar-tion of the earth were stopped.Stars would appearnearlyentpositionof the star.Themaximumwhichhasbeenstationary in the sky but would undergo a small annual cycleobserved isthatofBarnard's Star,which ismovingattherateofchangeduetoaberrationThemotionoftheearthinitsorbitof 10.3 seconds per year.This is a tenth-magnitude star, notissufficientlyfasttocausethe lightfrom starstoappearto shiftvisibleto the unaided eye.Of the 57 stars listed on the dailyslightlyinthedirectionoftheearth'smotion.Thisissimilartopages ofthealmanacs,Rigil Kentaurushas thegreatestproper motion, about 3.7 seconds per year.Arcturus,with 2.3the effect one experiences when walking in vertically-falling

236 NAVIGATIONAL ASTRONOMY ter of the sun is a stated number of degrees below the celestial horizon. Three kinds of twilight are defined: civil, nautical and astronomical. The conditions at the darker limit are relative and vary considerably under different atmospheric conditions In Figure 1516d, the twilight band is shown, with the darker limits of the various kinds indicated. The nearly ver￾tical celestial equator line is for an observer at latitude 20°N. The nearly horizontal celestial equator line is for an observer at latitude 60°N. The broken line in each case is the diurnal circle of the sun when its declination is 15°N. The relative duration of any kind of twilight at the two lat￾itudes is indicated by the portion of the diurnal circle between the horizon and the darker limit, although it is not directly proportional to the relative length of line shown since the projection is orthographic. The duration of twi￾light at the higher latitude is longer, proportionally, than shown. Note that complete darkness does not occur at lati￾tude 60°N when the declination of the sun is 15°N. 1517. Apparent Motion Due To Revolution Of The Earth If it were possible to stop the rotation of the earth so that the celestial sphere would appear stationary, the effects of the revolution of the earth would become more notice￾able. In one year the sun would appear to make one complete trip around the earth, from west to east. Hence, it would seem to move eastward a little less than 1° per day. This motion can be observed by watching the changing po￾sition of the sun among the stars. But since both sun and stars generally are not visible at the same time, a better way is to observe the constellations at the same time each night. On any night a star rises nearly four minutes earlier than on the previous night. Thus, the celestial sphere appears to shift westward nearly 1° each night, so that different con￾stellations are associated with different seasons of the year. Apparent motions of planets and the moon are due to a combination of their motions and those of the earth. If the ro￾tation of the earth were stopped, the combined apparent motion due to the revolutions of the earth and other bodies would be similar to that occurring if both rotation and revolu￾tion of the earth were stopped. Stars would appear nearly stationary in the sky but would undergo a small annual cycle of change due to aberration. The motion of the earth in its orbit is sufficiently fast to cause the light from stars to appear to shift slightly in the direction of the earth’s motion. This is similar to the effect one experiences when walking in vertically-falling rain that appears to come from ahead due to the observer’s own forward motion. The apparent direction of the light ray from the star is the vector difference of the motion of light and the motion of the earth, similar to that of apparent wind on a mov￾ing vessel. This effect is most apparent for a body perpendicular to the line of travel of the earth in its orbit, for which it reaches a maximum value of 20.5". The effect of ab￾erration can be noted by comparing the coordinates (declination and sidereal hour angle) of various stars through￾out the year. A change is observed in some bodies as the year progresses, but at the end of the year the values have returned almost to what they were at the beginning. The reason they do not return exactly is due to proper motion and precession of the equinoxes. It is also due to nutation, an irregularity in the mo￾tion of the earth due to the disturbing effect of other celestial bodies, principally the moon. Polar motion is a slight wobbling of the earth about its axis of rotation and sometimes wandering of the poles. This motion, which does not exceed 40 feet from the mean position, produces slight variation of latitude and longitude of places on the earth. 1518. Apparent Motion Due To Movement Of Other Celestial Bodies Even if it were possible to stop both the rotation and revolution of the earth, celestial bodies would not appear stationary on the celestial sphere. The moon would make one revolution about the earth each sidereal month, rising in the west and setting in the east. The inferior planets would appear to move eastward and westward relative to the sun, staying within the zodiac. Superior planets would appear to make one revolution around the earth, from west to east, each sidereal period. Since the sun (and the earth with it) and all other stars are in motion relative to each other, slow apparent motions would result in slight changes in the positions of the stars rel￾ative to each other. This space motion is, in fact, observed by telescope. The component of such motion across the line of sight, called proper motion, produces a change in the appar￾ent position of the star. The maximum which has been observed is that of Barnard’s Star, which is moving at the rate of 10.3 seconds per year. This is a tenth-magnitude star, not visible to the unaided eye. Of the 57 stars listed on the daily pages of the almanacs, Rigil Kentaurus has the greatest prop￾er motion, about 3.7 seconds per year. Arcturus, with 2.3 Twilight Lighter limit Darker limit At darker limit civil –0°50' –6° Horizon clear; bright stars visible nautical –0°50' –12° Horizon not visible astronomical –0°50' –18° Full night

237NAVIGATIONALASTRONOMYsecondsperyear,has thegreatestpropermotion ofthenavi-of approximately equal length all overthe earth.The wordgational stars in the Northern Hemisphere. In a few thousand"solstice,"meaning"sun stands still,"is applied because theyears proper motion will be sufficientto materially altersun stops its apparent northward or southward motion andsomefamiliar configurations of stars, notably Ursa Major.momentarily“stands still"before it starts in the oppositedi-rection.Thisaction,somewhatanalogoustothe“standof1519.TheEclipticthe tide, refers to the motion in a north-south direction onlyand not to thedaily apparent revolution around theearth.The ecliptic is the path the sun appears to take amongNote that it does not occur when the earth is at perihelion orthe stars dueto the annual revolution ofthe earth in its orbitaphelion. Refer to Figure 1519a. At the time of the vernalIt is considered a great circle of the celestial sphere, inequinox,the sun isdirectly overthe equator,crossingfromclined at an angle of about 23°26' to the celestial equator,theSouthernHemispheretotheNorthernHemisphere.Itrisbut undergoing a continuous slight change.This angle ises due east and sets due west, remaining above the horizoncalled the obliquity of the ecliptic.This inclination is duefor approximately 12 hours.It is not exactly12 hours be-to thefact thatthe axis ofrotation ofthe earth is not perpen-causeof refraction, semidiameter,and the heightof the eyedicularto its orbit. It is this inclination which causes the sunoftheobserver. These cause it to be above the horizon ato appear to move north and south during the year, givinglittle longer than below the horizon.Following the vernalthe earth its seasons and changing lengths of periods ofequinox, the northerly declination increases, and the sundaylight.climbs higher in the sky each day (at the latitudes of theRefer to Figure 1519a. The earth is at perihelion earlyUnited States), until the summer solstice,when a declina-inJanuaryandat aphelion6monthslater.OnoraboutJunetion ofabout23°26'northofthe celestial equator isreached21, about 10 or 11 days before reaching aphelion, the north-The sun then gradually retreats southward until it is againern part of the earth's axis is tilted toward the sun.The northover the equator at theautumnal equinox,at about 23°26polar regions are having continuous sunlight, the Northernsouthofthecelestialequatoratthewintersolstice.andbackHemisphere is having its summer with long, warm days andover thecelestial equator again at the nextvernal equinox.short nights; the Southern Hemisphere is having winterThe sun is nearest the earth during the northern hemi-with short days and long,cold nights, and the south polarsphere winter, it is not the distance between the earth andregion is in continuous darkness.This is the summer sol-sunthatisresponsibleforthedifferenceintemperaturedur-stice.Three monthslater,about September 23,theearth hasing the different seasons.The reason is to be found in themovedaquarterof thewayaroundthesun, but its axis ofaltitude of the sun in the sky and the length of time it re-rotation still points in about the samedirection in space.mains above thehorizon.During the summer the rays areThesunshinesequallyonbothhemispheres,anddavsandmore nearly vertical, and hence more concentrated, asnights are the same length over the entireworld.The sun isshown in Figure 1519b. Since the sun is above the horizonsetting at the North Pole and rising at the South Pole. Themore than half the time,heat is being added by absorptionNorthern Hemisphere is having its autumn, and the South-during a longerperiod than it is being lost byradiation.Thisern Hemisphere its spring.This is the autumnal equinoxexplains thelag ofthe seasons.Following the longest dayIn anotherthree months, on or about December 22, thethe earth continues to receivemore heat than it dissipates,Southern Hemisphere is tilted toward the sun and condi-but ata decreasingproportion.Graduallytheproportionde-tions are the reverse of those six months earlier, thecreases until a balance is reached, after which the earthNorthernHemisphereishavingitswinter.andtheSoutherncools, losing more heat than it gains. This is analogous toHemisphere its summer.This is the winter solstice.Threethe day,when the highesttemperatures normallyoccur sev-months later, whenbothhemispheresagainreceive equalamounts of sunshine,the Northern Hemisphere is havingeral hours after thesunreaches maximum altitudeatmeridian transit.A similar lag occurs at other seasons of thespring and the Southern Hemisphereautumn,the reverse ofconditions six months before.This is the vernal equinox.year.Astronomically,the seasons begin at the equinoxesThe word"equinox,"meaning“equal nights,"is apand solstices.Meteorologically,they differ fromplacetoplied because it occurs at the time when days and nights areplace

NAVIGATIONAL ASTRONOMY 237 seconds per year, has the greatest proper motion of the navi￾gational stars in the Northern Hemisphere. In a few thousand years proper motion will be sufficient to materially alter some familiar configurations of stars, notably Ursa Major. 1519. The Ecliptic The ecliptic is the path the sun appears to take among the stars due to the annual revolution of the earth in its orbit. It is considered a great circle of the celestial sphere, in￾clined at an angle of about 23°26' to the celestial equator, but undergoing a continuous slight change. This angle is called the obliquity of the ecliptic. This inclination is due to the fact that the axis of rotation of the earth is not perpen￾dicular to its orbit. It is this inclination which causes the sun to appear to move north and south during the year, giving the earth its seasons and changing lengths of periods of daylight. Refer to Figure 1519a. The earth is at perihelion early in January and at aphelion 6 months later. On or about June 21, about 10 or 11 days before reaching aphelion, the north￾ern part of the earth’s axis is tilted toward the sun. The north polar regions are having continuous sunlight; the Northern Hemisphere is having its summer with long, warm days and short nights; the Southern Hemisphere is having winter with short days and long, cold nights; and the south polar region is in continuous darkness. This is the summer sol￾stice. Three months later, about September 23, the earth has moved a quarter of the way around the sun, but its axis of rotation still points in about the same direction in space. The sun shines equally on both hemispheres, and days and nights are the same length over the entire world. The sun is setting at the North Pole and rising at the South Pole. The Northern Hemisphere is having its autumn, and the South￾ern Hemisphere its spring. This is the autumnal equinox. In another three months, on or about December 22, the Southern Hemisphere is tilted toward the sun and condi￾tions are the reverse of those six months earlier; the Northern Hemisphere is having its winter, and the Southern Hemisphere its summer. This is the winter solstice. Three months later, when both hemispheres again receive equal amounts of sunshine, the Northern Hemisphere is having spring and the Southern Hemisphere autumn, the reverse of conditions six months before. This is the vernal equinox. The word “equinox,” meaning “equal nights,” is ap￾plied because it occurs at the time when days and nights are of approximately equal length all over the earth. The word “solstice,” meaning “sun stands still,” is applied because the sun stops its apparent northward or southward motion and momentarily “stands still” before it starts in the opposite di￾rection. This action, somewhat analogous to the “stand” of the tide, refers to the motion in a north-south direction only, and not to the daily apparent revolution around the earth. Note that it does not occur when the earth is at perihelion or aphelion. Refer to Figure 1519a. At the time of the vernal equinox, the sun is directly over the equator, crossing from the Southern Hemisphere to the Northern Hemisphere. It ris￾es due east and sets due west, remaining above the horizon for approximately 12 hours. It is not exactly 12 hours be￾cause of refraction, semidiameter, and the height of the eye of the observer. These cause it to be above the horizon a little longer than below the horizon. Following the vernal equinox, the northerly declination increases, and the sun climbs higher in the sky each day (at the latitudes of the United States), until the summer solstice, when a declina￾tion of about 23°26' north of the celestial equator is reached. The sun then gradually retreats southward until it is again over the equator at the autumnal equinox, at about 23°26' south of the celestial equator at the winter solstice, and back over the celestial equator again at the next vernal equinox. The sun is nearest the earth during the northern hemi￾sphere winter; it is not the distance between the earth and sun that is responsible for the difference in temperature dur￾ing the different seasons. The reason is to be found in the altitude of the sun in the sky and the length of time it re￾mains above the horizon. During the summer the rays are more nearly vertical, and hence more concentrated, as shown in Figure 1519b. Since the sun is above the horizon more than half the time, heat is being added by absorption during a longer period than it is being lost by radiation. This explains the lag of the seasons. Following the longest day, the earth continues to receive more heat than it dissipates, but at a decreasing proportion. Gradually the proportion de￾creases until a balance is reached, after which the earth cools, losing more heat than it gains. This is analogous to the day, when the highest temperatures normally occur sev￾eral hours after the sun reaches maximum altitude at meridian transit. A similar lag occurs at other seasons of the year. Astronomically, the seasons begin at the equinoxes and solstices. Meteorologically, they differ from place to place

238NAVIGATIONALASTRONOMYROA(September)SummerSolstice(une)LmeSU8December)0WinterSolbsticem(Mareh)PFigure 1519a.Apparent motion of the sun in the eclipticnorthernhemisphere(astronomical)winteris shorterthanits summerbyabout seven daysEverywhere between the parallels of about 23°26'Nandabout23°26'S the sun is directlyoverhead at some timeduring the year. Except at the extremes, this occurs twice:once as the sun appears to move northward, and the secondtime as it moves southward. This is the torrid zone.Thenorthern limit is the Tropic of Cancer, and the southernlimit's theTropic of Capricorn.Thesenames comefromthe constellations which the sun entered at the solsticesuF8when the names were first applied more than 2,000 yearsago.Today,the sun is in the next constellation toward thewestbecauseof precession oftheequinoxes.TheparallelsJure 22about 23°26'from thepoles,marking theapproximatelim-its ofthe circumpolar sun, are called polar circles, the onein theNorthernHemispherebeingtheArcticCircleandtheone in the Southern Hemisphere the Antarctic Circle.Theareas inside the polar circles are the north and south frigidzones. The regions between the frigid zones and the torridzones are the north and south temperate zonesThe expression "vernal equinox"and associated ex-pressions are applied both to the times and points ofoccurrence of thevarious phenomena.Navigationally,Deeember22the vernal equinox is sometimes called the first point ofAries because, when the name was given, the sunFigure1519b.Sunlight in summer and winter.Compareentered the constellation Aries, the ram, at this time.Thisthe surface covered by the same amountof sunlight onpoint is of interest to navigators because it is the originthetwo dates.for measuring sidereal hour angle. The expressionsMarch equinox, June solstice, September equinox, andSince the earth travels faster when nearest the sun, theDecember solsticeareoccasionallyappliedasappropri-

238 NAVIGATIONAL ASTRONOMY Since the earth travels faster when nearest the sun, the northern hemisphere (astronomical) winter is shorter than its summer by about seven days. Everywhere between the parallels of about 23°26'N and about 23°26'S the sun is directly overhead at some time during the year. Except at the extremes, this occurs twice: once as the sun appears to move northward, and the second time as it moves southward. This is the torrid zone. The northern limit is the Tropic of Cancer, and the southern limit’s the Tropic of Capricorn. These names come from the constellations which the sun entered at the solstices when the names were first applied more than 2,000 years ago. Today, the sun is in the next constellation toward the west because of precession of the equinoxes. The parallels about 23°26' from the poles, marking the approximate lim￾its of the circumpolar sun, are called polar circles, the one in the Northern Hemisphere being the Arctic Circle and the one in the Southern Hemisphere the Antarctic Circle. The areas inside the polar circles are the north and south frigid zones. The regions between the frigid zones and the torrid zones are the north and south temperate zones. The expression “vernal equinox” and associated ex￾pressions are applied both to the times and points of occurrence of the various phenomena. Navigationally, the vernal equinox is sometimes called the first point of Aries because, when the name was given, the sun entered the constellation Aries, the ram, at this time. This point is of interest to navigators because it is the origin for measuring sidereal hour angle. The expressions March equinox, June solstice, September equinox, and December solstice are occasionally applied as appropri￾Figure 1519a. Apparent motion of the sun in the ecliptic. Figure 1519b. Sunlight in summer and winter. Compare the surface covered by the same amount of sunlight on the two dates

239NAVIGATIONALASTRONOMYate,because the more common names are associatedseconds per year)measured along the celestial equator,with the seasons in the Northern Hemisphere and are sixand precession in declination (about 20.04"per year)months outof step forthe Southern Hemisphere.measured perpendicular to the celestial equator.The an-The axis of the earth is undergoing a precessionalnual change in the coordinates of any given star,duetomotion similarto that ofa top spinning with its axis tilt-precession alone,depends upon its position on the celes-ed.In about 25,800 years theaxis completes a cycle andtial sphere, since these coordinates are measured relativereturnstothepositionfromwhichitstarted.Sincetheto the polar axis while the precessional motion is relativecelestial equator is 9oo from the celestial poles,it too isto the ecliptic axis.moving.Theresult isa slowwestwardmovement of theDue to precession ofthe equinoxes, the celestial polesequinoxes and solstices,whichhasalreadycarried themare slowlydescribing circles in the sky.The north celestialabout 3oo,or one constellation, along theecliptic frompole is moving closer to Polaris,which it will pass at a dis-thepositionsthey occupiedwhen namedmorethantance of approximately 28 minutes about the year 2102.2,000 years ago. Since sidereal hour angle is measuredFollowing this, the polar distance will increase, andeventu-from thevernal equinox,and declinationfromthe celes-ally other stars, in their turn, will become the Pole Star.tial equator,the coordinates of celestial bodies would beTheprecessionof theearth'saxis is theresultof grav-changing even if the bodies themselves were stationaryitational forces exerted principally by the sun and moon onThis westwardmotionof theequinoxes alongtheeclipticthe earth's equatorial bulge.The spinning earth responds tois called precession of the equinoxes.The total amount,theseforces in themannerofagyroscope.Regression ofthecalled general precession, is about 50.27 seconds pernodes introduces certain irregularitiesknown as nutation inyear (in1975).It may be considered divided into twocomponents:precession in rightascension (about 46.10theprecessional motion.1520.The Zodiacequation of time,is continually changing,theperiod ofdavlightisshiftingslightly,inadditiontoitsincreaseordeThe zodiac is a circular band of the sky extending 8crease in length due to changing declination.Apparent andon each side of the ecliptic.The navigational planets andmeansunsseldomcrossthecelestialmeridianatthesametime.The earliest sunset (in latitudes of the United States)themoonarewithintheselimits.Thezodiacisdividedintooccurs abouttwo weeks beforethewinter solstice,and the12 sectionsof30°each,each section being given the namelatest sunrise occurs abouttwo weeks after winter solsticeand symbol (sign")of a constellation.Theseare shown inFigure1520.Thenameswereassignedmorethan2.000Asimilarbut smallerapparentdiscrepancyoccursatthesummer solstice.years ago,when the sun entered Aries at the vernal equinoxUniversal Time is a particular case of the measureCancer at the summer solstice, Libra at the autumnal equi-nox,and Capricornus at the winter solstice.Because ofknown in general as mean solar time.Universal Time is theprecession,thezodiacal signs have shiftedwith respecttomeansolartimeontheGreenwichmeridianreckonedinthe constellations.Thus at thetime of thevernal equinox.days of24mean solarhoursbeginningwith0hours atmid-the sun is said to be at the“first point of Aries,"though it isnight. Universal Time and sidereal time are rigorouslyin the constellation Pisces.The complete list of signs andrelatedbyaformula sothat ifone isknowntheothercanbefound. Universal Time is the standard in the application ofnamesisgivenbelow.astronomytonavigation.1521.TimeAnd TheCalendarIf the vernal equinox is used as the reference,a sidere-al day is obtained, and from it, sidereal time. Thisindicatestheapproximatepositionsofthe stars,andforthisTraditionally,astronomyhas furnished thebasisforreason it is thebasis of star charts and starfinders.Becausemeasurement of time,a subject of primary importancetoof the revolution of the earth around the sun,a sidereal daythe navigator.The year is associated with the revolution ofthe earth in its orbit. The day is one rotation of the earthis about 3minutes56seconds shorter than a solarday,andthere is one more sidereal than solar days in a year.Oneabout its axis.mean solardayequals1.00273791mean sidereal days.BeTheduration of onerotation oftheearth depends uponcause of precession of the equinoxes, one rotation of thethe external reference point used. One rotation relative toearth with respect to the stars is not quitethe sameas onethe sun is called a solar day.However,rotation relative torotation withrespectto the vernal equinox.One mean solarthe apparent sun (the actual sun that appears in the sky)day averages 1.0027378118868 rotations of the earth withdoesnotprovidetimeofuniformratebecauseofvariationsrespect to the stars.in the rate ofrevolution and rotation of the earth.The errorIn tideanalysis,themoon is sometimes usedastherefdue to lack of uniform rate ofrevolution is removedby us-erence, producing a lunar day averaging 24 hours 50ing a fictitious mean sun.Thus,mean solar time is nearlyminutes (mean solar units)in length,and lunartimeequal to the average apparent solartime.Because the accu-mulateddifference between thesetimes,calledtheSince each kind of day is divided arbitrarily into 24

NAVIGATIONAL ASTRONOMY 239 ate, because the more common names are associated with the seasons in the Northern Hemisphere and are six months out of step for the Southern Hemisphere. The axis of the earth is undergoing a precessional motion similar to that of a top spinning with its axis tilt￾ed. In about 25,800 years the axis completes a cycle and returns to the position from which it started. Since the celestial equator is 90° from the celestial poles, it too is moving. The result is a slow westward movement of the equinoxes and solstices, which has already carried them about 30°, or one constellation, along the ecliptic from the positions they occupied when named more than 2,000 years ago. Since sidereal hour angle is measured from the vernal equinox, and declination from the celes￾tial equator, the coordinates of celestial bodies would be changing even if the bodies themselves were stationary. This westward motion of the equinoxes along the ecliptic is called precession of the equinoxes. The total amount, called general precession, is about 50.27 seconds per year (in 1975). It may be considered divided into two components: precession in right ascension (about 46.10 seconds per year) measured along the celestial equator, and precession in declination (about 20.04" per year) measured perpendicular to the celestial equator. The an￾nual change in the coordinates of any given star, due to precession alone, depends upon its position on the celes￾tial sphere, since these coordinates are measured relative to the polar axis while the precessional motion is relative to the ecliptic axis. Due to precession of the equinoxes, the celestial poles are slowly describing circles in the sky. The north celestial pole is moving closer to Polaris, which it will pass at a dis￾tance of approximately 28 minutes about the year 2102. Following this, the polar distance will increase, and eventu￾ally other stars, in their turn, will become the Pole Star. The precession of the earth’s axis is the result of grav￾itational forces exerted principally by the sun and moon on the earth’s equatorial bulge. The spinning earth responds to these forces in the manner of a gyroscope. Regression of the nodes introduces certain irregularities known as nutation in the precessional motion. 1520. The Zodiac The zodiac is a circular band of the sky extending 8° on each side of the ecliptic. The navigational planets and the moon are within these limits. The zodiac is divided into 12 sections of 30° each, each section being given the name and symbol (“sign”) of a constellation. These are shown in Figure 1520. The names were assigned more than 2,000 years ago, when the sun entered Aries at the vernal equinox, Cancer at the summer solstice, Libra at the autumnal equi￾nox, and Capricornus at the winter solstice. Because of precession, the zodiacal signs have shifted with respect to the constellations. Thus at the time of the vernal equinox, the sun is said to be at the “first point of Aries,” though it is in the constellation Pisces. The complete list of signs and names is given below. 1521. Time And The Calendar Traditionally, astronomy has furnished the basis for measurement of time, a subject of primary importance to the navigator. The year is associated with the revolution of the earth in its orbit. The day is one rotation of the earth about its axis. The duration of one rotation of the earth depends upon the external reference point used. One rotation relative to the sun is called a solar day. However, rotation relative to the apparent sun (the actual sun that appears in the sky) does not provide time of uniform rate because of variations in the rate of revolution and rotation of the earth. The error due to lack of uniform rate of revolution is removed by us￾ing a fictitious mean sun. Thus, mean solar time is nearly equal to the average apparent solar time. Because the accu￾mulated difference between these times, called the equation of time, is continually changing, the period of daylight is shifting slightly, in addition to its increase or de￾crease in length due to changing declination. Apparent and mean suns seldom cross the celestial meridian at the same time. The earliest sunset (in latitudes of the United States) occurs about two weeks before the winter solstice, and the latest sunrise occurs about two weeks after winter solstice. A similar but smaller apparent discrepancy occurs at the summer solstice. Universal Time is a particular case of the measure known in general as mean solar time. Universal Time is the mean solar time on the Greenwich meridian, reckoned in days of 24 mean solar hours beginning with 0 hours at mid￾night. Universal Time and sidereal time are rigorously related by a formula so that if one is known the other can be found. Universal Time is the standard in the application of astronomy to navigation. If the vernal equinox is used as the reference, a sidere￾al day is obtained, and from it, sidereal time. This indicates the approximate positions of the stars, and for this reason it is the basis of star charts and star finders. Because of the revolution of the earth around the sun, a sidereal day is about 3 minutes 56 seconds shorter than a solar day, and there is one more sidereal than solar days in a year. One mean solar day equals 1.00273791 mean sidereal days. Be￾cause of precession of the equinoxes, one rotation of the earth with respect to the stars is not quite the same as one rotation with respect to the vernal equinox. One mean solar day averages 1.0027378118868 rotations of the earth with respect to the stars. In tide analysis, the moon is sometimes used as the ref￾erence, producing a lunar day averaging 24 hours 50 minutes (mean solar units) in length, and lunar time. Since each kind of day is divided arbitrarily into 24